A =\(\cos^252\cdot\sin45+\sin^252\cdot\cos45\)
B=\(\tan15\cdot\tan75-\frac{\sin37}{\cos53}\)
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\(D=\cos45^0\cdot\cos^223^0+\sin45^0\cdot\cos^267^0\)
\(=\dfrac{\sqrt{2}}{2}\left(\cos^223^0+\cos^267^0\right)\)
\(=\dfrac{\sqrt{2}}{2}\)
\(A=\frac{\sqrt{2}}{2}cos^252+\frac{\sqrt{2}}{2}sin^252=\frac{\sqrt{2}}{2}\left(sin^252+cos^252\right)=\frac{\sqrt{2}}{2}\)
\(B=\sqrt{3}.cos^247+\sqrt{3}.sin^247=\sqrt{3}\left(sin^247+cos^247\right)=\sqrt{3}\)
b) \(S=\frac{1}{2}\sqrt{AB^2.AC^2-\left(\overrightarrow{AB}.\overrightarrow{AC}\right)^2}\)
\(=\frac{1}{2}\sqrt{AB^2.AC^2-AB^2.AC^2.cos^2A}\)
\(=\frac{1}{2}\sqrt{AB^2AC^2.sin^2A}\)
\(=\frac{1}{2}.AB.AC.\sin A\) (đpcm)
a ) \(x+x\times\frac{1}{3}\div\frac{2}{9}+x\div\frac{2}{7}=252\)
\(x\times1+x\times\frac{1}{3}\div\frac{2}{9}+x\div\frac{2}{7}=252\)
\(x\times1+x\times\frac{1}{3}\times\frac{9}{2}+x\times\frac{7}{2}=252\)
\(x\times1+x\times\frac{9}{6}+x\times\frac{7}{2}=252\)
\(x\times\left(1+\frac{9}{6}+\frac{7}{2}\right)=252\)
\(x\times6=252\)
\(x=252\div6\)
\(x=42\)
b ) \(\left(3\times x-0,8\right)\div x+14,5=15\)
\(\left(3\times x-0,8\right)\div x=15-14,5\)
\(\left(3\times x-0,8\right)\div x=0,5\)
\(0,8\div x=3-0,5\)
\(0,8\div x=2,5\)
\(x=0,8\div2,5\)
\(x=0,32\)